Volume 15, Issue 6

We present a research for Marangoni convection heat transfer in power law nanofluids driven by temperature gradient. Four types of nanoparticles, namely Cu, Al 2 O 3 , CuO and TiO 2 are considered by using power law CMC-water as a base fluid. The effects of power law viscosity on temperature field are taken into account by assuming that the temperature field is similar to the velocity field and the surface tension is assumed a quadratic function of the temperature. The governing partial differential equations are formulated and similarity solutions are obtained numerically using shooting method. The effects of the solid volume fraction, the Power law index and the Marangoni parameter on the velocity and temperature fields are analyzed and discussed in detail.

In this paper, n-species competitive system with impulsive effects is considered. Sufficient conditions are obtained for permanence, extinction and the existence and global attractivity of periodic solution. Some examples and numerical simulations are given.

This paper presents magnetohydrodynamic (MHD) stagnation point flow of second grade fluid over a permeable stretching cylinder. Analysis has been carried out with heat and mass transfer. Viscous dissipation and Joule heating effects are also investigated. Suitable transformations are used to convert non-linear partial differential equations into the non-linear ordinary differential equations. Variation of different parameters on the velocity, temperature and concentration profiles are shown graphically. Numerical values of skin friction coefficient, Nusselt number and Sherwood number are computed. Comparison of f ″(0), − θ ′(0) and − c ′(0) with the previous results are also examined.

In the present work, it is shown that the sequences obtained from a cryptographic sequence generator, the so-called shrinking generator, are just particular solutions of a type of linear difference equations. Moreover, all these sequences are simple linear combinations of m-sequences weighted by other sequences that correspond to the diagonals of the Sierpinski's triangle. These facts suggest a subtle link between irregular decimation and linearity that can be conveniently exploited in the analysis of cryptographic sequences. Previous ideas can be easily extended to other decimation-based cryptographic generators as well as to interleaved sequence generators.

Magnetoelastic behavior of a magnetic sensitive material has been analyzed theoretically in the present paper. The theory is formulated in the context of continuum electromagnetics. The solid medium is supposed to be made of elastic material with magnetic sensitivity and to be nonlinear, homogeneous, compressible, isothermal, has anisotropy. Magneto-elastic response of the material will show up as a stress and a magnetization field. From the formulation belonging to the constitutive equations, it has been observed that the stress and the magnetization have been derived from a scalar-valued thermodynamic potential defined in calculations. As a result of thermodynamic constraints, it has been determined that the free energy function is dependent on Green deformation tensor, magnetic field, and temperature distribution. The free energy function has been represented by a power series expansion and the type and number of terms taken into consideration in this series expansion has determined the non-linearity of the medium. Constitutive equations of symmetric stress, magnetization field and asymmetric stress have been obtained in both material and spatial coordinates. The quasi-linear constitutive equations which on material coordinates have been obtained by expressions (63)–(65). The quasi-linear constitutive equations have been given in expressions (70)–(72) on spatial coordinates. Finally, the quasi-linear constitutive equations of the symmetric stress and magnetization field are substituted in the relevant balance equations to obtain the field equations. The field equations containing the unknowns u k and ϕ coordinates have been obtained by expressions (75) and (76). Solution of these field equations under initial and boundary conditions forms the mathematical structure of specified a boundary value problem.

A new matrix spectral problem associated with sl(2,), which generalizes the Wadati-Konno-Ichikawa spectral problem, is introduced, and the corresponding hierarchy of soliton equations is generated from the associated zero curvature equations. A bi-Hamiltonian structure of the resulting generalized soliton hierarchy is furnished by using the trace identity, and thus, every system in the generalized hierarchy is Liouville integrable.

In this paper, we research the thermo-mechanical reliability of lead-free solder joints in WLCSP assembly subjected to an accelerated thermal cyclic loading based on finite element simulation and Taguchi method. Effects of different control factors, including solder materials, height of solder ball, chip thickness and substrates thickness on the reliability of the lead-free solder joints were examined and calculated. The corner solder joint is the most critical solder joints in the assembly, the top surface of the solder joint is the crack propagated location. The optimal design in the WLCSP assembly has the combination of the SnAgCuAl, height of solder ball at 0.25 mm, chip thickness at 0.6 mm, substrate thickness at 1.0 mm. Moreover, the solder materials is the most important factor among the control factors in the WLCSP assembly.